Instruction 15-1
A large organization randomly selects 150 employees and finds that 66% who have never taken a professional-development course would like such a course. The firm did a similar study 10 years ago in which 60% of a random sample of 160 employees wanted a professional-development course. The groups are assumed to be independent random samples. Let π 1 and π 2 represent the true proportion of workers who would like to attend a professional-development course in the recent study and the past study, respectively.
-Referring to Instruction 15-1,what is the value of the test statistic to use in evaluating the alternative hypothesis that there is a difference in the two population proportions using α = 0.10?
A) 1.194
B) 0.274
C) 4.335
D) 2.706

Question

Quizplus · Accepted Answer

The test statistic for comparing two proportions is calculated using the formula for the difference between two independent proportions. The formula is $Z = \frac{(\hat{p}_1 - \hat{p}_2)}{\sqrt{p(1-p)(\frac{1}{n_1} + \frac{1}{n_2})}}$, where $\hat{p}_1$ and $\hat{p}_2$ are the sample proportions, $n_1$ and $n_2$ are the sample sizes, and $p$ is the pooled proportion. Given the information, the calculation results in a test statistic of 1.194, which corresponds to choice A.

Instruction 15-1 A Large Organization Randomly Selects 150 Employees and Finds That